A device of this type is disclosed in U.S. Pat. No. 5,325,346. This device has a scanning means for scanning an optical disk, the output of which scanning means is connected to the input of an analogue-to-digital converter, whose output is in turn connected to the input of a mirror signal detector. For different track crossing frequencies, i.e. when the scanning means crosses tracks of the recording medium at a varying speed perpendicularly to the track direction, various delay elements are provided in a TZC signal path of the known device in order to compensate for influences on a signal obtained from the TZC signal and the mirror signal, which are caused by the track crossing frequency. The known device may be regarded as having the disadvantage that although it is suitable for track crossing frequencies of varying magnitude, a correctly generated mirror signal is assumed. Since it is precisely at particularly high track crossing frequencies that problems arise in the generation of the mirror signal itself, the known device is not suitable for such high track crossing frequencies.